Consider the decimal number 11.37510.
We already know that the binary
value of 11 is 10112. Now we need
to find the binary number for the fractional part 0.37510.
The steps below show how to convert this number to binary using repeated
multiplication.

First, we multiply 0.375 by 2 to find the most significant digit
(the rightmost digit). Since our result is less than 1, the most
significant digit in our answer is 0.

0.375*2 = 0.75

Answer:
0 .0??

Next, we take the fractional part of our previous result (0.75)
and multiply by 2 again. Now the result is greater than 1, so
the next digit of our answer is 1.

0.75*2 = 1.5

Answer:
0 .01?

Again we take the fractional part of our previous result (0.5)
and multiply by 2. This time our result is exactly 1, so the least
significant digit (the leftmost digit) is 1. Since the fractional
part of our result is 0, this is the last multiplication needed
to find our answer.

0.5*2 = 1.0

Answer:
0 .011

We can also organize this conversion in table form as we did with the
previous one.

Consider the decimal number 11.37510.
To find the binary value for this number we use both repeated
division on the integer part (11) and repeated
multiplication on the fractional part (0.375). Then we simply
combine the two binary values to get our answer of 1011.0112.

1011.0
+ 0.011
1011.011

It is important to note that many decimal fractions
do not have an exact representation in binary. For example, when we
convert the decimal fraction 0.110
to binary, our answer looks like this:

0.00011001100110011001100...

Notice how this binary fraction repeats infinitely. Since we cannot
represent some fractions exactly in binary, we cannot perform exact
arithmetic with fractions. You may not realize it, but your computer
actually has very tiny amounts of error in its computations. You rarely
see these errors because the binary approximations are very close to
the exact decimal value. However, when programmers write programs which
perform many mathematical computations, they must consider this error
to ensure their answers are reliable.